A Riemann type definition of a variational integral. (English) Zbl 0749.26006

Recently, the author has defined a coordinate free variational integral on bounded sets of finite perimeter, for which a quite general Gauss- Green theorem is valid [the author, Real Anal. Exch. 14, No. 2, 523-527 (1989; Zbl 0677.26007)]. A Riemann type definition was also given. The present paper shows that this variational integral possesses a simpler Riemann type definition which shows in particular that, in the special case of dimension one, the new integral properly lies between the Lebesgue and the Denjoy-Perron integral. The proofs use a lemma de Congedo-Tamanini on BV sets.


26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
26B15 Integration of real functions of several variables: length, area, volume


Zbl 0677.26007
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